If you can rotate (or turn) a figure around a center point by fewer than 360° and the figure appears unchanged, then the figure has rotation symmetry. The point around which you rotate is called the center of rotation, and the smallest angle you need to turn is called the angle of rotation.

This figure has rotation symmetry of 72°, and the center of rotation is the center of the figure:

Use the Interactive Activity to explore the rotation symmetry of the figures in Problem B1.

This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version, answer Problem B1 using your own observational skills.

Problem B1

a.

Each of these figures has rotation symmetry. Can you estimate the center of rotation and the angle of rotation?

b.

Do the regular polygons have rotation symmetry? For each polygon, what are the center and angle of rotation?

Video SegmentIn this video segment, watch the participants as they explore rotational symmetry and try to come up with the rule for regular polygons' rotational symmetry.

Were you able to come up with the rule? Does the rule work only for regular polygons or also for irregular ones?

If you are using a VCR, you can find this segment on the session video approximately 16 minutes and 49 seconds after the Annenberg Media logo. The second segment begins approximately 18 minutes and 30 seconds after the Annenberg Media logo.

As you will see in the next section, in order to have rotation symmetry, the center of rotation does not have to be the center of the figure. A figure can have rotation symmetry about a point that lies outside the figure.